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55^ NIST SPECIAL PUBLICATION 260" 1 42
U.S. DEPARTMENT OF COMMERCE/Technology Administration
National Institute of Standards and Technology
Standard Reference Materials®
Primary Standards and
Standard Reference Materials
for Electrolytic Conductivity
R. H. Jameel, Y. C. Wu, and K. W. Pratt
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NIST Special Publication 260-142
Standard Reference Materials®
Primary Standards and Standard Reference
Materials for Electrolytic Conductivity
R. H. Jameel
Y. C. WuK. W. Pratt
Analytical Chemistry Division
Chemical Science and Technology Laboratory
National Institute of Standards and Technology
Gaithersburg, MD 20899-8390
U.S. DEPARTMENT OF COMMERCE, William M. Daley, Secretary
TECHNOLOGY ADMINISTRATION, Dr. Cheryl L. Shavers, Under Secretary of Commerce for Technology
NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G. Kammer, Director
Issued February 2000
Certain commercial equipment, instruments, or materials are identified in this paper in
order to specify the experimental procedure adequately. Such identification is not intended
to imply recommendation or endorsement by the National Institute of Standards and
Technology, nor is it intended to imply that the materials or equipment identified are
necessarily the best available for the purpose.
National Institute of Standards and Technology Special Publication 260-142
Natl. Inst. Stand. Technol. Spec. Publ. 260-142, 46 pages (Feb. 2000)
CODEN: NSPUE2
U.S. GOVERNMENT PRINTING OFFICEWASHINGTON: 2000
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
Primary Standards and Standard Reference Materials for Electrolytic Conductivity
R. H. Jameel, Y. C. Wu, K. W. Pratt
National Institute of Standards and Technology
Gaithersburg, MD 20899-8390
Abstract
This report describes the principles and methods for measuring the electrolytic conductivity
of primary standards and NIST Standard Reference Materials (SRMs). There are two methods for
measuring conductivity: the direct current (DC) method, and the alternating current (AC) method.
NIST has redetermined the conductivity of the primary standards, and determined a set of molality-
based primary standards over a temperature range of 0 °C to 50 °C. The conductivities of the
primary standards were determined using two uniquely designed conductivity cells for measuring
resistance with the AC and DC methods. The primary standards are used to determine the cell
constants of conductivity cells. In our laboratory, we used both Jones and Daggett cells for
measuring conductivity. NIST issues a set of Standard Reference Materials (SRMs) available in
nominal conductivity values of 5 uS/cm, 15 uS/cm, 25 uS/cm, 100 uS/cm, 500 uS/cm,
1 000 uS/cm, 10 000 uS/cm, 20 000 uS/cm, and 100 000 uS/cm. The certified conductivity values
for the SRMs include the solvent conductivity.
Keywords: AC; benzoic acid; conductivity; conductivity cell; DC; electrolyte; hydrochloric acid;
standards; potassium chloride; primary standards; non-aqueous solvent
iii
Contents
Abstract iii
Glossary vii
1 . Introduction 1
1 . 1 Principles of the Electrolytic Conductivity Measurement 1
1 .2 Equivalent Conductivity 2
1.3 Electrolytic Conductivity of Water 4
2. General Scheme of the Electrolytic Conductivity Measurement 5
2.1 Temperature Control 5
2.2 Carbon Dioxide Contribution 6
2.3 Evaporation and Transpiration 7
3. Absolute Conductivity Measurements 8
3.1 Primary Standards 8
3.2 AC Absolute Method 11
3.2.1 Cell Design 12
3.2.1.1 Cell Cleaning Process 14
3.2.2 Instrumentation 15
3.2.3 Measurement 17
3.3 DC Absolute Method 18
v
3.3.1 Cell Design 18
3.3.2 Instrumentation 19
3.3.3 Measurement 22
3.4 AC vs. DC Method 23
3.5 Error Analysis for Primary Standards 24
4. AC Conductivity Measurement With Other Cells 26
4.1 Cell Construction 26
4.2 Calibration of Cells 28
4.2. 1 Cells With Constants Greater Than 1 .5 cm"1
28
4.2.2 Cells With Constants Less Than 1 .5 cm"1
28
4.3 Measurement and Instrumentation 30
5. Conductivity Standards for Industrial Applications 31
5.1 Commercial Standards 31
5.2 Standard Reference Materials (SRMs) 31
5.2. 1 Preparation and Measurements of SRMs 32
5.2.2 Error Analysis for SRMs 33
5.3 Low Conductivity Standards 34
6. Discussion and Conclusion 36
7. References
vi
38
Glossary
A constant for an electrolyte solution based on Kohlrausch's Square Root Law
A effective cross-sectional area
c concentration, units are specified as either mol/L, equivalents/L, or mol/kg
Ej potential between the potential electrodes in the DC conductance cell
£s potential drop across the standard resistor in DC measurement
AE average potential difference between two center Ag, AgCl electrodes in DC cell
F force under which an ion moves
/ current
/ ionic strength (Section 1 .2 only)
A'ceii cell constant of a conductivity cell
A'ceii. t cell constant of the center tube of either an AC or DC absolute conductivity cell
ATceu. w cell constant of AC absolute conductivity cell with center tube
A'ceii, n cell constant of AC absolute conductivity cell without center tube
/ effective length between electrodes
q mobility function (Eq. 9)
R resistance
Ru resistance of a solution in the AC absolute conductivity cell without center tube
Rs resistance of standard resistor used in the DC absolute measurement
Rj resistance of a solution in the center tube of the DC absolute conductivity cell
Rw resistance of a solution in the AC absolute conductivity cell with center tube
r radius of a sphere as defined by Stokes' Law
T absolute temperature
vii
/ temperature, °C
// mobility of an ion
v velocity of a sphere as defined by Stokes' Law
Z valence of an ion
z.\ valence of a cation
Z2 valence of an anion
e dielectric constant
77 viscosity of a homogenous medium
k electrolytic conductivity of an electrolyte solution
Kba electrolytic conductivity of benzoic acid
Kkci electrolytic conductivity of potassium chloride
A equivalent conductivity of an electrolyte
A0equivalent conductivity of an electrolyte at infinite dilution
A ionic equivalent conductivity
X° ionic equivalent conductivity at infinite dilution
X° ionic equivalent conductivity at infinite dilution of a cation
Xi ionic equivalent conductivity at infinite dilution of an anion
p resistivity
(0 frequency
viii
X. Introduction
Electrolytic conductivity is the measure of a solution's ability to conduct current. The
magnitude of the conductivity is dependent on the nature of the ions (i.e., charge, size and mobility)
and the nature of the solvent (such as dielectric constant and viscosity). The electrolytic
conductivity is a result of ionic movement in a particular solvent, which is related to the ionic
interactions taking place within the solution. The measurement of electrolytic conductivity is a
nonspecific measurement; all ions contribute to the electrolytic conductivity of the solution.
In order to have uniform conductivity measurements, accurate electrolytic conductivity
standards must be available for industrial use. For this purpose, the National Institute of Standards
and Technology (NIST) has developed a series of electrolytic conductivity Standard Reference
Materials (SRMs) and issues them through its Standard Reference Materials Program. This report
describes the theory and practice for preparing SRMs.
1.1 Principles of the Electrolytic Conductivity Measurement
The measurement of a solution's resistance, /?, in a conductivity cell, is used to determine
the conductivity of a solution. The resistance of a solution is proportional to the distance between
the electrodes, /, and inversely proportional to the effective cross-sectional area, A:
R = p — ,ohm (1)A
The resistivity, p, is a constant for a given solution and is expressed in units of ohm-cm.
Conductivity is defined as the reciprocal of resistivity:
K = — =—— ,ohm"' cm"1
orScm"1
(2)
p R A
The cell in which the conductivity is measured has a cell constant, A^eii, which is defined as
=~> cm "'
(3)A
where / is the effective length between the electrodes and A is the effective cross sectional area. A
useful definition for the electrolytic conductivity, K, is obtained by combining Eq. (1-3),
KT = ^!L ,Scm'' (4)R
where R is the resistance of the solution and ATcen is the cell constant.
Generally, a cell can be constructed in any shape; however, the cell volume and the
positions of the electrodes must be rigidly fixed and, therefore, the effective physical dimensions of
a cell, the / and A, are constant. The cell constant is determined by measuring the geometrical
dimensions of the cell or by comparing with primary standard solutions in the cell. In the first case,
/ and A are measured directly. In the second case, the cell constant is determined from Eq. (4) with
known fcand R. To determine the absolute standards, Kohlrausch measured the cell constant
mechanically [1-3]. Jones and Bradshaw [4] used mercury, which then defined the international
ohm, to determine their cell constants. Both of these measurements have been reviewed and the
primary standards for determination of the cell constant were recommended [5].
NIST reconfirmed the old set of standards [6] and established a new set of primary
standards. The new primary standards are based on the molality scale. The conductivity value for
each standard has been determined at a wider range of temperatures than formerly available. In the
following sections, a detailed description of these measurements will be given and discussed.
1.2 Equivalent Conductivity
Often, referring to equivalent conductivity, A, of a solution as opposed to electrolytic
conductivity is desirable. The equivalent conductivity is related to the solution's ionic concentration.
2
A =1000k-
,Scm 2
equiv1
(?)
c
where c is the concentration of the electrolyte expressed in equivalents per liter. The International
Union of Pure and Applied Chemistry (IUPAC) has recommended that molar conductivity be used
in place of equivalent conductivity. However, the electrolytic conductivity theory was developed in
terms of equivalent conductivity and much of the data in the early work was reported in terms of
equivalent conductivity. The old usage has been retained here to avoid confusion.
The equivalent conductivity, A, is the sum of the individual ionic conductivities, A,
at infinite dilution, A0, is the sum of the individual ionic conductivities at infinite dilution, A
0.
Kohlrausch's Law of Independent Migration of Ions states that when ions are far enough apart that
the movement of one ion is not influenced by other ions present in solution, the ions are at infinite
dilution [7].
Conductivity is dependent on the concentration of the electrolyte in solution. The equivalent
conductivity of a strong electrolyte generally increases with increasing concentration due to an
increase in the number of ions present. For strong electrolytes in dilute solution, the equivalent
conductivity may be expressed emperically by the Kohlrausch Square Root Law [7]:
A = \ +X, + ... + An (6)
where the equivalent conductivity has units of cm 2£T' equiv"
1
.Similarly, the equivalent conductivity
A = A'-Ajc (7)
3
where A is an empirical constant for a given electrolyte. Later, Onsager [8] used Debye-Hiickel's
ionic theory to develop a limiting law for equivalent conductivity with the same form as Eq. 7, but
with a theoretical value for the constant A
A =2801000|z
1z 2
|<?yl" 41.25(jz,| + |z 2 |)
(£7)4 +^)+
ipo41 (8)
where
kz 2 |X' + x^
and z\ is the valency of the cation, z2 is the valency of the anion, £ is the dielectric constant, r\ is the
viscosity, T is the absolute temperature, and / is the ionic strength.
1.3 Electrolytic Conductivity of Water
The electrolytic conductivity of an electrolyte solution consists of the conductivity of the
solvent and the conductivity of the solute. Hence, the conductivity of water (typically the solvent) is
important. The equivalent conductivity, A, of pure water at 25 °C is 0.055 uS cm2equiv"'[9].
Equation (5) can be used to calculate the theoretical electrolytic conductivity of water. For
water at 25 °C, the p/^w = 14 and therefore, the concentration of H+and OH" ions from dissociated
water molecules is cH+ = <:0h- = 10"7equivalents per liter. The X° for H+
is 349.81 S cm2equiv"
1
and
the A0for OH" is 198.3 S cm 2
equiv"1
[7]. The electrolytic conductivity of water is calculated by
K*« =K* + Kh~ = [198.3 + 349.81 ]Scm 2equivalent
1
=549.11 S cm 2equivalent"
1
Ac 549 xlO"7
k = = S/cm = 5.5 x 1
0"8S/cm = 0.055 uS/cm
1000 1000
This theoretical value is difficult to obtain experimentally because atmospheric CO2 is readily
absorbed into water. The conductivity of C02 in water was measured and found to be 1 .05 uS/cm
4
at 25 °C [8,10]. When other ionic contaminants are also present in water, the conductivity value
will increase further. For example, when 1 ppm of Ca++
ions, or Na+ions, is present in water (c «
5x105equivalents per liter), the conductivity of this water would be approximately 3 |iS/cm. In
addition to the 1 |iS/cm from CO2 absorption, the final value for the conductivity of water would be
4 |iS/cm. Thus, the value of conductivity is an indicator for the purity of water if this value is
properly determined. To ascertain the accuracy of the measured value, low conductivity standards
are needed for calibration and for quality assurance of the purity of water (see Sec. 5.3).
2. General Scheme of the Electrolytic Conductivity Measurement
The conductivity of a solution is determined by measuring the resistance of a solution in
a given cell, using either the AC or DC method, and then calculating the conductivity from
Eq. (1). The AC method uses a Wheatstone bridge for measuring the resistance, and the DC
method uses a DC digital voltmeter (DVM). The details of the AC and DC methods will be
described in Sec. 3. The electrolytic conductivity of a solution is affected by the temperature of
the solution, the carbon dioxide content of the solution, and the amount of evaporation or
transpiration that occurs prior to the measurement.
2.1 Temperature Control
Electrolytic conductivity is very sensitive to changes in the temperature of the solution. The
conductivity of inorganic electrolytes changes about 2 % for each degree Celsius at room
temperature [7]. A 0.005 °C fluctuation will cause a ±0.01 % change in conductivity. Therefore,
good temperature control is required for an accurate measurement of the conductivity of a solution.
To achieve the required temperature control, the conductivity cell is placed in a constant
temperature bath. Mineral oil is typically used as the bath fluid. The equipment used at NIST for
monitoring the temperature of the constant temperature bath consists of a quartz thermometer
5
connected to a frequency counter with a digital readout. The quartz thermometer and frequency
counter were calibrated by comparison to the NIST standard platinum resistance thermometer
(SPRT) and have an uncertainty not greater than 0.002 °C. When the temperature bath is correctly
adjusted, the temperature can be controlled to ±0.002 °C.
When the conductivity cell is designed such that there are large electrodes in bulbs at the end
of a long narrow tube, most of the resistance is contributed by the narrow tube. The effect of
temperature, t, on the cell constant is given by [7]
where Og = 3.6 x 10"6 °C', the thermal expansion coefficient of Pyrex glass. For the whole range of
temperatures, 0 °C to 50 °C, the change in A^eii is approximately 0.02 %. This method of
determining the cell constant has been used in our laboratory for determining the temperature effect
on the cell constant of an absolute conductivity cell.
2.2 Carbon Dioxide Contribution
The electrolytic conductivity of pure water equilibrated with atmospheric carbon dioxide
is typically taken to be 1 uS/cm [9]. Carbon dioxide will dissolve in solution producing H+and
HCO3", which will contribute to the conductivity of the water. The contribution of these ions to
the conductivity is referred to as Kqo-,- The concentration of these ions is dependent on the
atmospheric pressure, ventilation, and number of people in a particular laboratory. When
conditions vary, the uncertainty in Kfco-, is taken as 20 % of the typical value for the conductivity
of water in equilibrium with atmospheric C(X Therefore, for an aqueous KC1 solution, the
(10)
6
uncertainty in Kco-,is estimated to be ±0.2 uS/cm. The lower pH of the HC1 solution suppresses
carbon dioxide dissociation.
In a nonaqueous-aqueous solvent, carbon dioxide dissolution and hydrogen ion
conductivity is much less than that in water. Typically, the variation in Kco2is less than
±0.1 uS/cm [9].
When NIST electrolytic conductivity SRMs are prepared, the solution is shaken for
several days to facilitate equilibration with carbon dioxide prior to bottling. The certified value
of the batch includes the contributions to the conductivity of all ions present in the solution,
including HCO3 . Therefore, the user does not need to degas the solution prior to use. By
equilibrating the solution with atmospheric carbon dioxide, the need to prepare and measure the
solution in a carbon dioxide free environment is avoided, making the SRMs easier to use.
2.3 Evaporation and Transpiration
Transpiration and evaporation both cause the conductivity of a solution to increase.
Transpiration, the passage of solvent through containers, has been observed in this laboratory for
bottles made of low-density polyethylene (LDPE). Solutions that will be stored for more than a
day, such as an SRM, should be packaged such that minimal transpiration occurs over the time of
storage. In this laboratory, glass bottles are used for SRMs because the amount of transpiration,
if any, is unnoticeable. For solutions that will be used immediately after they are prepared, such
as primary standards, transpiration is much less of a concern since long-term storage is not an
issue.
Evaporation may occur as a result of the measurement process, or as a result of a poor
packaging technique. When preparing the solution or filling the cell, evaporation needs to be
minimized. For primary standards, accurate concentration is necessary for accurate
7
measurement. This is much less of a concern for electrolytic conductivity SRMs, which are
certified based on conductivity and not on exact concentration. Filling the cell, with any
solution, will cause slight evaporation of the solution. Evaporation may also occur if the cap of
the bottle is not completely closed, or if the cap relaxes and loosens with time. In this laboratory,
such problems have been noted for glass bottles with polypropylene caps and glass bottles with
Bakelite caps. However, serum bottles and ampoules do not appear to have a problem with
evaporation when they are sealed.
To obtain an accurate measurement of the conductivity of a solution, evaporation and
transpiration must be minimized. Over time, if evaporation and transpiration due to the
packaging of the solution occurs, the accuracy of the conductivity measurement will be
compromised.
3. Absolute Conductivity Measurements
Absolute conductivity measurements are performed using conductivity cells, the cell
constant of which is determined by basic standards only (electrical and physical). The two
absolute methods, AC and DC, use different types of cells and instrumentation. The choice of
the AC or DC method will be described in Sec. 3.4. The absolute conductivity measurement has
been used at NIST to determine the conductivity of molality-based primary standards. These
primary standards may then be used to calibrate other types of cells (section 4).
3.1 Primary Standards
Establishment of conductivity values for primary standard solutions requires the use of the
absolute method, and is the primary purpose of the absolute method. Both the AC and DC methods,
described in the following sections, have been used to measure the conductivity of the primary
8
standards. The work performed in this laboratory [8, 10-12], and described in this report, has taken
several years. The data are listed in Tables 1-3.
Table 1. Definition of Demal for 0.0 ID, 0.1D, and 1.0 D KC1 Solutions
Demality grams of KC1 per kilogram of
0.01 0.7458 19<6)
0.1 7.47458(6)
1.0 71.1352(8)
Table 2. Electrolytic Conductivity Values for 0.01 D, 0.1D, and 1.0 DKC1 Solutions* and Water, ITS-90 Scale
t/°C 104
k:/ (jiS/cm)
0.01 D KCl(fI)0.1 D KC1 1.0 D KC1 (8) H2
0^0 773.09 713.46 65 135 0.58
5 891.17 819.97 73 860 0.68
10 1 014.2 930.82 82 871 0.79
15 1 141.7 1 045.6 92 136 0.89
18 1 220.1 1 116.1 97 804 0.95
20 1 273.2 1 163.8 101 620 0.99
25 1 408.4 1 285.1 1 1 1 300 1.10
30 1 546.8 1 408.9 121 110 1.20
35 1 688.0 1 535.0 131 050 1.30
40 1 831.5 1 662.8 141 080 1.40
45 1 976.9 1 791.9 151 150 1.51
50 2 123.8 1 921.9 161 240 1.61
* Values of conductivity for KC1 solutions do not include solvent conductivity
9
i
I
i
I
Table 3. Electrolytic Conductivity Values for the Molality-Based Primary Standard KC1 Solutions*
0.01 mol/kg, 0.1 mol/kg, and 1.0 mol/kg, ITS-90 Scale
t/°C10
4Kl (|nS/cm)
0.01 mol/kg 0.1 mol/kg 1.0 mol/kg water
value(10)
2uc(U) valued value
(8)2«c
(12)value
(10)
0 0.23 2.85 63 487 25 0.58
5 0.27 3.27 72 030 29 0.68
10 1 013.95 0.30 3.72 80 844 32 0.79
15 1 141.45 0.34 10 437.1 4.2 89 900 36 0.89
18 1 219.93 0.37 11 140.6 4.5 0.95
20 1 273.03 0.38 11 615.9 4.6 99 170 40 0.99
25 1 408.23 0.42 12 824.6 5.1 108 620 43 1.10
30 1 546.63 0.46 14 059.2 5.6 118 240 47 1.20
35 1 687.79 0.51 15 316.0 6.1 127 970 51 1.30
40 1 831.27 0.55 16 591.0 6.6 137 810 55 1.40
45 1 976.62 0.59 17 880.6 7.2 147 720 59 1.51
50 2 123.43 0.64 19 180.9 7.7 157 670 63 1.61
*Values of conductivity for KC1 solutions do not include solvent conductivity
Primary standards are used for calibrating conductivity cells. The chief requirement for the
standard is accuracy. The factors affecting the accuracy of the primary standards include stability of
the chemical, purity of the solute and solvent, and concentration of the solution. Potassium chloride
was chosen as the solute [1-6] because KC1 is stable and easily purified. Water is used as the
solvent because it is also stable and easily purified. These two factors are very important for
maintaining uniformity and repeatability when the solutions are prepared in different laboratories,
so that the results can be accurately compared. For high accuracy measurements, the concentration
of the primary standard solutions should be accurate to at least 5 places.
Currently, three primary standards at three temperatures are recommended by IUPAC [13]
and Organization Internationale de Metrologie Legale (OLML). These primary standards are based
10
on the measurements of Jones and Bradshaw [4]. The primary standards have concentrations
defined by the so-called demal (D) scale, which is defined as an exact mass of KC1 in an exact mass
of water. This scale is not related to any other concentration scale. The demal unit is defined at
three concentrations only (Table 1): 0.01 D, 0.1 D, and 1.0 D.
NIST redetermined the primary standards adopted by IUPAC and determined a new set of
molality-based primary standards. The measurements of the primary standards by Jones and
Bradshaw were performed over 60 years ago and several basic standards have been changed.
Moreover, the demal scale lacks a direct relationship to the common units of concentration and to
the units used in solution chemistry. The original values have been adjusted for changes in the basic
standards to obtain the values currently adopted by IUPAC. In addition, the conductivities of the
recommended demal standards are only determined at three temperatures. Therefore, NIST not
only redetermined the set of primary standards adopted by IUPAC to reconfirm its value, but also
determined a set of molality-based primary standards available at temperatures from 0 °C to 50 °C
at 5 °C intervals and at 18 °C (Table 3) to expand the applicability of primary standards.
The molality-based primary standards developed at NIST were prepared using potassium
chloride and water. Molality, mol/kg, is defined as the amount of solute in one kilogram of solvent
in vacuo. Molality-based primary standards at three concentrations expressed in molality
(0.01 mol/kg, 0.1 mol/kg, and 1 .0 mol/kg) in the temperature range of 0 °C to 50 °C have been
proposed to OIML and to the IUPAC for adoption [10,12].
3.2 AC Absolute Method
The AC absolute cell was designed and constructed at NIST for the measurement of the
0.01 D and 0.1 D primary standards, and the 0.01 mol/kg and 0.1 mol/kg molality-based primary
11
standards [6,10,1 1]. This AC absolute cell, its design, instrumentation, and measurement
method, are described in the following sections.
3.2.1 Cell Design
The AC absolute cell, shown in Fig. 1 , is a Jones type cell with a removable center tube.
Figure 1 . AC absolute conductivity cell: a, a - electrode chambers (half-cells); b - removable
center extension tube; c, c - flanges; d, d - platinum disk electrodes; e, e - O-rings. The mating
flange ends are held together by a C-shaped Bakelite band (not shown) so that lateral movement is
prevented.
The design of this cell allows determinations of the conductivity of a solution from basic standards.
No calibration of the cell is necessary. The details of cell construction [9,10] are briefly described
as follows. A length of precision-bore 1 cm I. D. Pyrex tubing, with uniformity certified by the
manufacturer, was cut into 3 sections. A prefabricated flange, c, with an I. D. of 1.3 cm, O. D. of
2.5 cm, and thickness of 0.65 cm was epoxied into each of the tubes such that the face of the flange
was flush with the cut end of the tube. Then, each flanged end was ground to optical flatness. The
unflanged end of each of the singly flanged tubes was joined to the corresponding electrode
chamber, a, each of which contained a 2 cm platinum disk electrode, d. The electrodes were gold
soldered to a 2 mm platinum wire, which extended through a graded-glass seal. To assemble the
12
cell, the mating flange ends are held together by a C-shaped Bakelite band which can be slightly
enlarged with a little pressure, such that the two flanges fit snugly into it, preventing the flanges
from moving laterally. Lateral and rotational movements are prevented by a Bakelite two-plate
assembly tightened together with four nylon screws and nuts. A rubber O-ring, e, is inserted
between each plate and the rear side of the flange. The tube b of the cell is removable, and its
dimensions (length and internal diameter) were determined by the Length and Mass Division of
NIST (presently, length is determined by the Precision Engineering Division; mass is determined by
the Automation Production and Technology Division).
Since the cell constant in a Jones-type conductance cell is determined by the lines of force
between the two electrodes, the center section of the tube may be removed in order to shorten the
distance between the electrodes, thereby reducing the resistance. Subsequently, the same section
may be put back, lengthening the distance and increasing the resistance, provided that the lines of
force are not disturbed. Thus, there are essentially two cells: one is with the center tube b, and the
other is without the center tube b. When the conductivity, K, of a solution with fixed concentration
is measured with the two cells, we will obtain the resistance of the solution in the cell with the
center tube, /?w ,
cell.wK = (IDK
and the resistance of the solution in the cell without the center tube, R^,
cell.N
(12)K
13
where /fceii.w and KCd\, n are the cell constants with and without the center tube, respectively.
Similarly, /?w and RN are measured resistances when using the cell with the center tube and without
the center tube, respectively.
Equation (11) and Eq. (12) may be combined by subtracting from /?w and solving for jc
/?w -RN /?w - fl N
The cell constant of the center tube, ATCeii,T = IIA, is determined by physical measurements of / and A
and is equal to ATce ii, w - ATce n. N . All the quantities on the right-hand side of Eq. (13) are known by
means of physical measurement. Therefore /cis absolutely determined and values for Kce\], w and
A^eiLN can then be calculated from Eq. (11) and Eq. (12).
3.2.1.1 Cell Cleaning Process
When the cell is newly constructed, it is cleaned with chromic acid cleaning solution, rinsed
with water, soaked in a 6 mol/L HC1 solution for 1 h, washed with water, soaked in distilled water
overnight, and dried at room temperature. In cases where the HC1 soaking, water washing, soaking,
and vacuum drying do not remove the last traces of adsorbed chromate ions, the process must be
repeated. (Strong acids and organic solvents have been tried as a replacement for chromic acid
cleaning solution, without success.) After the cell is thoroughly clean and dry, it is assembled and
filled with a standard KC1 solution. If no leak is detected at the joints after the filled cell stands for
1 h, the cell is put into the bath for 30 min to 40 min until the solution reaches thermal equilibrium
with the bath temperature. The reading is then recorded. If no drift is noted over a 1 h period, the
cell is emptied and refilled to obtain measurements in triplicate. If the deviation of the results is less
than 0.01 % and random, the mean is taken as the final result. If the deviation shows a trend toward
increasing or decreasing resistance, there are two probable causes: cell contamination and loss of
14
water from the solution by evaporation. Cell contamination is generally caused by adsorption of
foreign substances on the cell walls and/or electrodes. There is no easy way out of this except either
to repeat the experiment until the foreign substances are leached out and the readings are constant,
or to repeat the cleaning process. If the drift is due to concentration increase by evaporation, a new
solution will generally cure it.
The procedures for changing from one concentration to another and/or for replacing the
center tube of the cell are similar. The cell is taken out from the bath, the outside wall of the cell and
the whole assembly are washed with soap solution and rinsed with water. The inside of the cell is
flushed with distilled water continuously for about 30 min. The whole unit is dried with paper
towels and is disassembled. The joints of the cell are cleaned with soap and water. When everything
is dry, they are re-assembled. Caution is always exercised to prevent the oil on the outside of the cell
from creeping inside. If this occurs, the cleaning process must be repeated.
3.2.2 Instrumentation
The AC method for conductivity measurement consists of a constant temperature bath and
the resistance measurement instrumentation. The constant temperature bath used when measuring
the primary standards [1 1] is briefly described below. The bath consisted of a rectangular, steel,
open-top box surrounded by a wood cabinet with a hinged cover that can be opened or closed. The
space between the sides of the steel box and the wood cabinet was insulated with glass wool.
Within the steel box were vertical, open-ended rectangular walls around which a piece of copper
tubing was looped. The tubing led to the outside of the wood cabinet for connection to a
temperature-controlled fluid. A stirrer was mounted on the inside wall to provide good circulation.
Studs were mounted in the front side of the steel box to allow for support and manipulation of the
conductivity cell. Twenty gallons of petroleum oil were used as bath fluid, and the oil was changed
15
every 6 months to 8 months. Water was circulated through the copper coil and back for cooling by
an auxiliary constant-temperature bath. The heating is facilitated with a quartz heater submerged
into the bath. The whole unit was connected to a proportional temperature control unit. A
thermistor is used as the sensor for the temperature controller. A quartz thermometer and frequency
counter are used as the bath temperature indicator.
The AC instrumentation [10,1 1] is described as follows. The AC measurement uses a Jones
bridge [14,15], which is a Wheatstone bridge with capacitance compensation that is specifically
designed for conductivity measurements. The Jones bridge is equipped with a capacitor and resistor
in parallel to balance the impedance of the conductivity cell. The bridge also employs a Wagner
ground to minimize the effects of stray capacitance on the accuracy of the null point. The ratio-
arms are held exactly equal.
Alternating current is supplied to the bridge by a signal generator. The signal generator can
be operated from 20 Hz to 15 kHz. The normal operating range of frequency, ft), is 1 kHz to 5 kHz.
The resistance is corrected for the effect of polarization by plotting R versus ft)1
and extrapolating to
a) = oo [7]. The signal generator was modified by floating the secondary of the output transformer to
obtain an ungrounded output, which is required to make use of the Wagner ground of the Jones
bridge. A single-ended (unbalanced) output was obtained from a secondary winding of the output
transformer and was used as the phase reference for the detector. The applied AC voltage to the
bridge is 1.2 V RMS. A differential input preamplifier, tuned amplifier, and oscilloscope are used
in the detector circuit. The differential input of the preamplifier preserves the balance of the
Wagner ground and eliminates the need for an input transformer. The tuned amplifier is used in the
bandpass mode at a Q (Q is the ratio of the frequency to the bandwidth, thus, the smaller the
bandwidth, the larger the Q) of 10 to 50, to attenuate the second and higher harmonics at the null
16
point. The output of the tuned amplifier and the reference signal from the signal generator are
connected to the vertical and horizontal inputs of the oscilloscope, respectively. The displayed
pattern on the oscilloscope is a Lissajous figure and is used to indicate both capacitive and resistive
balance of the bridge simultaneously [16]. (The technique was superior to using the in-phase and
quadrature output meters of the lock-in amplifier to indicate resistive and capacitive balance of the
bridge.)
With this setup, a 0.001 % change in cell resistance may be detected on the oscilloscope.
Hence, a change of 0.001 °C in the bath temperature (0.002 % in R) can be observed. The
uncertainty in the null point measurement did not contribute significantly to the overall uncertainty
of the measurement of the resistance of the primary standard.
3.2.3 Measurement
In the AC measurement of conductivity, the cell will generally have an impedance Z\ that is
not purely resistive. However, there are other sources of impedance such as the Parker effect [17]
and the effect of a conducting thermostat medium [14]. These effects can be avoided by proper cell
design.
When measuring the resistance of a solution, the combination of the solution conductivity
and cell constant is chosen such that the measured resistance is within the optimum range of
resistances for the bridge. The optimum range for resistances when using the Jones bridge is
1 000 Q. < R < 10 000 Q. The Jones bridge has five decade resistors plus the slide wire resistor. The
maximum uncertainty of the nominal readings of the dials is less than 0.005 % as stated by the
manufacturer.
The cell is placed into the conductivity bath for about 30 min, so that the solution in the cell
can reach thermal equilibrium with the temperature of the bath. Resistance readings are taken at 1
17
kHz and 2 kHz at 10 min intervals to determine that the solution's temperature is constant. The
polarization correction is made by plotting the measured resistance, R, vs. ft)1
and extrapolating to
l/ft)= 0 [7]. The resistance of the solution is then calculated by correcting the extrapolated
resistance for the lead resistance (from the electrodes to the binding posts of the bridge). If the
resistance continuously drifts upward or downward for 30 min, this indicates that the concentration
of ions in the solution is changing, or that the temperature is changing. In this instance, the
measurement should be stopped, the cause of the drift determined, and the measurement repeated.
3.3 DC Absolute Method
At NIST, the DC absolute cell was designed for the measurement of the 1 D primary
standard and the 1 mol/kg molality-based primary standard [8]. The DC absolute cell, its design,
instrumentation, and measurement method, are described in the following sections.
3.3.1 Cell Design
The DC absolute cell is a four-electrode conductivity cell (Fig. 2). The two inner electrodes
are used to measure potential drop and the outer two electrodes are used to measure the applied
current, /. In order to eliminate polarization effects, all four electrodes must be reversible to the
solution. For primary standard KC1 solutions, Ag, AgCl electrodes are suitable.
For an absolute determination of conductivity, the cell constant needs to be determined with
the same basic standards (e.g., length measurement) as the AC cell. To accomplish this
requirement, a precision bore Pyrex tubing is cut into three pieces, so that the center section of the
cell could be removed and that the internal diameter and length of this center section could be
measured accurately by physical methods. The two ends of the center section were polished to
flatness, while the surfaces of the ends of the other two pieces, which will join with the center
section, were ground to a roughness of about 25 um. A slight gap was formed between the joined
18
ends of the tubing to effect a miniscule flow of solution, when the sections are rejoined using a
nylon union. The other two ends of the cut tubing are fused to Pyrex tubing comprising the current
compartments of the cell. A U-shaped capillary separates the current-electrode chamber from the
connecting chamber to minimize the effect of electrolysis products on the measurement. A third
tube is joined at each of the junctions of the center section with the end sections using a nylon-union
tee. These compartments contain the potential leads for the measurements. The final assembly is
shown schematically in Figure 2.
1 2 2 1
Figure 2. DC Absolute conductivity cell: 1,1- current electrodes; 2, 2 - potential difference
sensing electrodes; 3 - nylon tee joints; 4,4 - O-rings.
Cleaning of the cell when it is newly constructed, and when changing concentrations, is the
same as described in Sec. 3.2. 1 .
1
3.3.2 Instrumentation
The DC method is much simpler in principle than the AC method and is determined by
Ohm's law [8]. A high precision digital voltmeter (DVM), an accurate standard resistor, and a
constant current supply are needed for the measurement of R. Both the DVM and the standard
resistor were calibrated by the Electricity Division at NIST. The constant current supply can
19
provide current from 25 uA to 250 mA and has a stability of ±0.005 % over 14 h. A schematic
diagram of the operating circuit is shown in Fig. 3.
d
Figure 3. Schematic of DC Operating and Switching Circuitry: a - conductivity cell with gaps A,
A; b - digital voltmeter; c - constant current supply; d - switch with position 1 and 2; e - switch
with position 3 and 4; /?s- standard resistor
With switch d in the 2 position and switch e in the 3 position, current flows through the standard
resistor and the conductance cell, and the 1R drop across the standard resistor, £s , is measured by the
DVM as
ES=1R
S (14)
where R& is the resistance of the standard resistor and / is the current. / is thus determined. Moving
switch d to the 1 position while switch e remains in the 3 position effects the measurement of the
voltage between the potential electrodes in the conductance cell, Ej,
ET= IRT (15)
where Rj is the resistance of the solution in the conductance cell. Switching e to the 4 position
reverses the flow of current and the polarity of the current electrodes. A data point at a singe
20
current consisted of four measurements as shown in Table 4. Any difference between the standard
redox potentials, £°, of the potential difference-sensing electrodes was eliminated by reversing the
direction of the current, /, and averaging the magnitudes of the two measured potential differences.
This averaged potential difference, AE, was related to conductivity by
where Kce\\ j is the cell constant of the center tube, and Rj is the resistance of the solution in tube.
Table 4. Measurement Sequence'
Measurement Switch d Switch e
1 2 3
2 1 3
3 1 4
4 2 4
Two pairs of matched Ag, AgCl electrodes were used in the conductance cell: one pair for the
current electrodes and the other for the potential electrodes. The preparation and calibration of these
electrodes have been described in conjunction with the pH studies at NIST [18]. All four electrodes
were within ± 0.05 mV of each other. Reversible electrodes are required to eliminate polarization
effects. Ag, AgCl electrodes, appropriate for KC1 solutions, were used for all four electrodes to
minimize the effects of electrolysis and polarization.
Two constant temperature baths were used at NIST: an oil bath [10] in which the
temperature could be controlled to ±0.002 °C (described in Sec. 3.2.2) and a water bath [1 1] in
21
-
which the temperature could be controlled to ±0.001 °C to ±0.002 °C for temperatures above
0°C.
3.3.3 Measurement
After the cell is assembled, and filled with solution, the electrodes are placed in the
appropriate chambers. The whole cell assembly is put into the bath, and its temperature is adjusted
and controlled as designated. Usually, the starting temperature is 25.000 °C, and a steady state is
reached after about 30 min.
The wiring to the electrodes was connected according to the scheme shown in Fig. 3. The
outer electrodes are connected to a constant current supply, c. A standard resistor, Rs , is inserted
between an outer electrode and the constant current supply, so that the current passing through the
cell and the Rs is the same (see Fig. 3). The inner electrodes are connected to the digital voltmeter,
b. The gaps, A, are the opening for connecting the inner electrodes (Fig. 3). Platinum wires may
serve as the outer electrodes. The inner electrodes are preferably reversible to the electrolyte
solution, such as Ag/AgCl to KC1, in order to eliminate polarization. For a solution without
reversible electrodes, e.g., NH4NO3, calomel electrodes with liquid junction may be used to measure
the potential drop across the fixed points a. The cell is modified with four side tubes to
accommodate the liquid junction at the inner electrodes, and to minimize the hydrolysis effect at the
outer electrodes.
It took approximately 3 s for a reading, and there were four readings for a selected current,
two each for each direction (as described in Sec. 3.3.2). Each data point was taken as the mean of
three different currents. At each temperature, the current flowed through the cell for approximately
30 s. Thus, the power dissipated in the cell was less than 1 mW, and its effect was much smaller
22
than a millidegree per second change for the solution. Therefore, there is no significant heating
effect.
3.4 AC vs. DC Method
For absolute measurement of conductivity, there are limitations of dimension for the
constant temperature bath and for the conductivity cell. Hence, the range of cell constants is
limited. Thus, the AC method is preferred for solutions of low conductivity and high resistance
due to lower experimental uncertainties. The DC method is preferred for solutions of high
conductivity, and hence low resistance. For the AC method, an optimum range of resistance is
required for the best accuracy. Typically, an error in the resistance of a few hundredths of an
ohm would result from either the bridge or the lead resistance. For example, if R is 100 Q, an
error of 0.05 Q absolute is equivalent to an error of 0.05 % relative. If R is 1000 Q, an error of
0.05 Q. absolute is equivalent to an error 0.005 % relative. Therefore, a larger cell constant,
which is difficult to achieve, is necessary when using the AC method to minimize these effects.
When the DC method is used, errors due to the bridge and the lead resistance are eliminated.
Because the potential measured does not include the leads, the lead resistance is eliminated. The
accuracy of a voltmeter can reach 10"7 to 10"8 V. An applied current may be selected from 10"5 to
10 " A. For a given cell constant, Kcan be varied a thousandfold and can be determined without
sacrificing accuracy.
The conductivities of the 1 mol/kg molality-based primary standard and the 1 D primary
standard were determined using the DC method (Table 2-3). The conductivities of the 0.01 mol/kg
and 0.1 mol/kg molality-based primary standards and the 0.01 D and 0.1 D primary standards were
determined using the AC method (Table 2-3).
23
3.5 Error Analysis for Primary Standards
The error analysis performed at NIST for the conductivity measurements of the molality-
based primary standards using the AC and DC measurement methods [6,8-1 1] is briefly discussed
below. The errors calculated for each value of conductivity [12] are listed in Table 3. The values for
the conductivity of the primary standards (Table 3) were calculated using Eq. (17), which is a
polynomial fit of the values for conductivity at each temperature:
K = a + bt + ct2+dt* (17)
The values for a, b, c, and d are given in Table 5. The standard uncertainty of the differences
between the smoothed values of jcand the discrete values of /care 0.0046 %, 0.0126 %, and
0.0145 % for the 0.01 mol/kg, 0.1 mol/kg, and 1.0 mol/kg molality-based KC1 primary standards,
respectively.
Table 5. Parameters in the Polynomial Fit for Electrolytic Conductivity Versus Temperature*
Molality, mol/kg Parameters
a b c d
0.01 0.0772921 2.30846 x 10"-' 1.07715 x 10"5 -5.84084 x 10"*
0.1 0.711685 2.09002 x 102
8.99144 x 10"' -5.07124 x 10"'
1.0 6.34882 1.6913 x 101
6.00781 x 10"4 -3.83702 x 10"°
The uncertainty in the measurements of#cen, t was based on the measurement of the length and
diameter of the tube. The values for the standard uncertainty are 0.0065 % for 0.01 mol/kg and
0.1 mol/kg, and 0.0085 % for the 1.0 mol/kg molality-based primary standard.
24
The effect of changes in temperature on A'ceii.T may be calculated from Eq. (10), which
applies to both AC and DC measurements. For the AC measurements, the values of jcfor each
molality were calculated using the corrected value of A'ceii.T- The uncertainty in this correction for
AC measurements was negligible. For the DC measurements, no correction was applied to A'ceii.T-
The standard uncertainty is taken as 0.0052 % for the DC measurements, based on the estimated
change in A'ce ii, t with temperature.
The uncertainty in the measurement of temperature, arising from the calibration of the
thermometer, was ±0.002 K. The temperature coefficient at each temperature was determined
directly from the smoothed polynomial fit of k-
versus t. The largest temperature coefficient, which
was at 0 °C, was multiplied by ±0.002 K. The standard uncertainty, ±0.0034 %, was treated as a
uniform probability distribution, and has been divided by 3>/2
[19].
The effect of impurities in the KC1 for the primary standards was estimated to contribute an
uncertainty of 0.0025 % to the conductivity. The standard uncertainty due to evaporation of the
primary standard solutions during transfer to the conductivity cell is estimated to be 0.0025 %.
The resistors in the AC conductivity bridge were calibrated and the uncertainty in this
calibration, 0.001 %, was treated as a uniform probability distribution. The standard uncertainty
was thus taken as 0.0057 %. The standard uncertainty of the DC measurements of current and
potential was taken as 0.00061 %.
The uncertainty in the solvent correction was taken as 0.2 uS/cm. The standard uncertainty,
treated as a uniform probability distribution, was less than 0.0015 % in all cases.
The uncertainties for each primary standard were calculated as the root sum of squares. The
actual uncertainties were conservatively estimated to be 0.03 % for the 0.01 mol/kg primary
25
standard, and 0.04 % for both the 0.1 mol/kg and 1 .0 mol/kg primary standards. Uncertainties
calculated for each primary standard at each temperature are given in Table 3.
4. AC Conductivity Measurement With Other Cells
As mentioned in Sec. 3, the primary standards are used to calibrate conductivity cells.
Absolute cells are used when the best possible accuracy is needed. Some solutions, such as
SRMs, do not require the high accuracy measurement that primary standards require. For SRMs,
Jones and Daggett cells [7], which are calibrated using primary standards, are used for making
the resistance measurements.
4.1 Cell Construction
The Jones and Daggett cells used at NIST are made of borosilicate glass and use platinum
electrodes. Jones cells are usually composed of two glass bulbs, each containing a platinum disk
electrode, separated by a piece of glass tubing to give a large cell constant (Fig. 4).
Figure 4. Jones Cell: Jones cell is similar to the AC absolute cell except that it does not have a
removable center tube.
To minimize evaporation when filling the cell, the solution is poured through a funnel and into
the cell. Less evaporation occurred with this type of filling than with the other methods
examined in this laboratory.
26
Daggett cells consist of an Erlenmeyer flask that is connected to a glass bulb containing
the electrodes (Fig. 5). The use of the Erlenmeyer flask facilitates filling of the cell.
Figure 5. Daggett cell: diagram is similar to the Jones cell, except that an Erlenmeyer flask is
attached to facilitate filling of the cell.
However, an Erlenmeyer flask can only be attached to cells with small cell constants due to
design problems. Daggett cells are typically used for low conductivity solutions.
All of the Jones and Daggett cells used at NIST were made on-site. Several items must
be considered when making a conductivity cell. The cells should contain no rough edges and
ridges. Any microcracks where the solute could be trapped must also be eliminated. When
adding a solution to the cell, any trapped solute would dissolve and the concentration of ions, and
therefore the conductivity, would change. Two types of microcracks were observed with
commercial cells: ( 1 ) at the joining of the platinum wire to the disk, and (2) at the joining of the
platinum to the glass. The lack of a smooth surface when spot welding the platinum disk onto the
platinum lead left small cracks where KC1 could be trapped. These cracks were eliminated by
using gold to smooth out the surface. Because Pyrex does not wet platinum, the glass would pull
away from the lead leaving small cracks where KC1 could be trapped. This problem was solved
27
by using a type of soda lime glass that does wet platinum. A graded seal was used to fuse the
soda lime glass to Pyrex.
4.2 Calibration of Cells
Presently, the Jones and Daggett cells at NIST have cell constants ranging from about
0.05 cm'1
to 1 10 cm"1
. The standards used for calibrating these cells must be accurately
prepared, as was mentioned in Sec. 3.1 for the primary standards. Solutions should be used
within several hours of preparation to minimize evaporation and transpiration. Several different
standard solutions should be used and, when possible, at least two of the solutions should have
concentrations that are one order of magnitude different. The cell should be calibrated at the
temperature, or temperatures, that will be used for measuring the conductivity of solutions.
4.2.1 Cells With Constants Greater Than 1.5 cm 1
For calibrating a cell at 25 °C, molality-based primary standards are available in the
conductivity range of approximately 1 400 uS/cm to 1 10 000 uS/cm. The combination of solution
and cell should result in a resistance in the optimum range. This is easily achieved for cells with
A'ceii > 1.5 cm"1
. For example, a cell with #ce n = 2 cm'1
would be calibrated with the primary
standard having a molality of 0.01 mol/kg which has a conductivity of 1409.33 uS/cm, including
the solvent conductivity. In this example, the measured resistance would be about 1 400 £1. A
cell with A'ceii = 1 10 cm"1
would be calibrated with the primary standard having a molality of
1 .0 mol/kg. The measured resistance would be about 1 000 Q.
4.2.2 Cells With Constants Less Than 1.5 cm"1
As mentioned above, for calibrating a cell at 25 °C, primary standards are available in the
conductivity range of approximately 1 400 uS/cm to 1 10 000 uS/cm. If #ce ii^ 1-5 cm"', the
resistances of the primary standards will be in the range of 900 Q. to 10 Q. The accuracy of a
28
resistance measurement would be compromised because an uncertainty of ±0.1 Q. in the measured
resistance would cause a 0.014 % to 1 % uncertainty in conductivity. If the primary standard is
used for calibrating a cell with A^ii ~ 0.1 cm"1
, the uncertainty will increase according to Eq. (4).
Therefore, working solutions must be used.
At NIST, working solutions are prepared for calibrating conductivity cells by estimating the
amount of KC1 necessary to give the desired conductivity. The resistance of the working solution is
then measured in a cell that was calibrated with a primary standard. The conductivity of the
working solution is calculated from Eq. (4). The resistance of the same working solution is then
measured in the cell to be calibrated. Since the conductivity of the working solution is known, the
cell constant may be calculated from Eq. (4).
Some workers in this field employ the Onsager limiting law equation [5,20] for KC1 as a
function of concentration to prepare secondary standards of the desired conductivity. The
equivalent conductivity is calculated for the low concentration of aqueous potassium chloride so
that a solution of low conductivity, and optimum resistance, may be used to calibrate the cell. The
equivalent conductivity of KC1 solutions having concentrations less than 0.05 moles/L may be
calculated by
AKC!
= 149.83 -95.09Vc+ 38.66c logc + 183.9c (18)
where c has units of mol/L and y\Kci has units of Sm2/mol. Equation ( 1 8) is based on the literature
values for A° [5] and has been corrected for the change from international ohm to the absolute ohm,
the change 1948 EPTS units to 1990 IPTS units, the change in the liter unit, and changes in the
atomic masses of K and CI. The electrolytic conductivity is calculated from Eq. (5). Thus, for a
KC1 solution of molality 0.0001 mol/kg, k= 14.888 u.S/cm, not including the solvent conductivity.
29
If Keen is approximately 0.05 cm"1
, then R is approximately 3 400 Q, which is in the range of
optimum resistance. This calibrating equation may yield reasonable accuracy provided the
preparation and measurement of the solution are done with pure water and under a C02 free
atmosphere. Under these conditions, the solvent conductivity correction is near the theoretical
value, i.e., 0.055 |iS/cm. Otherwise, the solution conductivity must be corrected for a solvent
conductivity of 1 . 1 uS/cm with an uncertainty of ±0. 1 uS/cm to ±0.3 |iS/cm. This solvent
correction would cause an uncertainty of 7 % for a solution having k= 14.888 uS/cm.
HC1 solutions may also be used for calibrating a cell that has a low cell constant. The
theoretical equation [21] for calculating the conductivity of dilute HQ can be written as:
AHC1 =426.16-158.68V? + 185.60clogc + 500c (19)
At 0.0001 mol/L, Kis 42.46 (iS/cm for a cell with Kce \\~ 0.05 cm"
1
and the resistance measured
would be approximately 1 200 Q. Since the HC1 solution has a lower pH than an aqueous KC1
solution, CO2 dissociation is suppressed. Therefore, the uncertainty due to the solvent correction is
much smaller. In a carbon dioxide free environment, Eq. (19) yields reasonable accuracy.
4.3 Measurement and Instrumentation
In general, the Jones and Daggett cells are used at NIST to measure the conductivity of
SRMs. Measurements made to calibrate the cell or to determine the conductivity of a solution
use the instrumentation as described for the AC absolute method (Sec. 3.2.2 and Sec. 3.2.3).
When first constructed, the cell is cleaned as described in Sec. 3.2.1.1. Prior to a
measurement, the cell may be cleaned by soaking with water and drying under clean air, argon,
or nitrogen. A clean, dry cell is typically rinsed 3 times with the solution to be measured prior to
filling the cell. In this laboratory, when several solutions are to be measured in a row, such as
30
when certifying an SRM, cleaning and drying the cell is not practical due to the amount of time
required. Rinsing the cell 5 times with the solution to be measured is sufficient to remove any
noticeable effects of the solution previously in the cell.
5. Conductivity Standards for Industrial Applications
When the high accuracy of primary standards discussed in Sec. 3.1 is not needed,
commercial standards are sufficient. The most common application of conductivity standards is cell
calibration. Two types of industrial standards for electrolytic conductivity are available:
commercial standards, many of which claim NIST traceability, and NIST SRMs. The standards
must be readily available and easy to use.
5.1 Commercial Standards
Commercial standards are available at conductivities from 100 uS/cm to 100 000 uS/cm.
The uncertainties of some of these standards can be as high as 0.5 %.
5.2 Standard Reference Materials (SRMs)
To satisfy industrial needs, NIST certifies and issues certifies a series of electrolytic
conductivity SRMs. The SRMs may be divided into two groups: aqueous (nominal values of
25 uS/cm, 100 uS/cm, 500 uS/cm, 1 000 uS/cm, 10 000 uS/cm, 100 000 uS/cm, 20 000 uS/cm),
and mixed aqueous-nonaqueous (5 uS/cm and 15 |iS/cm). The conductivity of these standards
includes the solvent conductivity.
All but two of the aqueous SRMs are prepared as KC1 in water. The solute for the 25 uS/cm
solution is hydrochloric acid. Hydrochloric acid is used for lower conductivity solutions because it
suppresses carbon dioxide dissociation at its low pH. The solute for the 20 000 uS/cm solution is
NaCl. The use of NaCl was specifically requested by clinical laboratories. When the 20 000 uS/cm
31
solution is made with NaCl, the ionic strength of the solution approximates the ionic strength of
body fluid.
The two lowest conductivity SRMs are prepared using KC1 in 30 % n-propanol 70 % water.
These SRMs are discussed further in Sec. 5.2.3.
5.2.1 Preparation and Measurement of SRMs
The SRMs are prepared initially by underestimating the amount of solute needed for a given
amount of solvent that will give the desired conductivity. Since the SRMs are certified based on
conductivity, the exact concentration of ions, or more specifically KC1, is not critical. Any minor
contamination of the bulk solution (prior to certification) will not spoil the SRM. The bulk solution
is then shaken for several days to ensure that the solution is homogenous, and to ensure that the
solution has equilibrated with atmospheric C02 . Using the AC method (Sec. 3.2.2 and Sec. 3.2.3)
and a calibrated Jones or Daggett cell (Sec. 4), the resistance of a sample of the bulk solution is
measured over several hours. If there is no drift in the conductivity, the solution is equilibrated with
atmospheric CCX The concentration is then adjusted by adding solute or solvent as required to get
closer to the nominal value of conductivity.
The solution is bottled, typically yielding 80 units of the SRMs. A stratified random
sampling, based on the bottling order, is used to determine which units will be measured. The
measurements of these units are randomized so that trends in bottling order and measurement order
may be differentiated. The mean value of these units is called the determined value. This
determined value is adjusted upward to correct for changes in the conductivity due to evaporation
and/or transpiration, and leaching as needed, to yield the final certified value.
32
5.2.2 Error Analysis for SRMs
The calculation of the certified value for SRMs has recently been reevaluated. For SRMs,
the uncertainty consists of 5 components: 1 ) random variations in the measurement of conductivity,
2) standard uncertainty of the cell constant, 3) resistance measurements, 4) temperature fluctuation
observed during the measurements, and 5) carbon dioxide contribution to the conductivity of the
solution. Depending on the bottling type, the effects of transpiration, evaporation, and leaching
must also be considered. The uncertainties for each SRM are expressed in absolute terms in each
SRM certificate. To generalize the uncertainties for all SRMs, most of the standard uncertainties
described below are expressed in relative terms, and are only approximations. A complete
uncertainty analysis is required for each SRM batch to determine the uncertainty portion of the
certified value of the given SRM.
The random variation in the measurement of conductivity is determined from the standard
deviation of the mean and is generally less than 0.008 %. The combined standard uncertainty of the
cell constant from a complete uncertainty analysis is used as the standard uncertainty of the cell
constant.
The standard uncertainty in the resistance measurements is stated by the manufacturer of the
conductivity bridge to be ±0.005 % RforR> 100 Q. (95 % confidence interval).
The standard uncertainty of small resistances measured with the digital voltmeter, such as
the lead resistance, is stated by the manufacturer of the digital voltmeter to be 0.0012 Q, absolute.
The standard uncertainty for temperature is taken as the temperature variation observed while
making the resistance measurements, which is typically ±0.002 °C. The standard uncertainty of the
lead resistance and temperature is modeled as a uniform probability distribution and is, therefore,
divided by f\
33
The standard uncertainty due to the thermometer calibration has not previously been
included in the determination of the uncertainty of a given SRM. The standard uncertainty of the
thermometer calibration is typically 0.002 °C for 95 % confidence interval.
The standard uncertainty of the contribution of CO2 to the total conductivity is estimated
from the possible existing conditions in users' laboratories. The concentration of CO2 is highly
environmentally sensitive and, therefore, can vary due to changes in temperature, atmospheric
pressure, and laboratory ventilation. In addition, the CO2 concentration in a laboratory is higher if
more people are in the laboratory. The variation in concentration of CO2 is estimated to give a
variation of ±0.2 uS/cm, absolute, in solvent conductivity. This uncertainty is also modeled as a
uniform probability distribution.
Transpiration and evaporation are major concerns when determining the value of an
SRM. Unlike primary standards which should be prepared and used immediately, SRMs may
not be used for several months after they are packaged. The appropriate packaging must be
chosen to minimize the effects of evaporation and transpiration.
5.3 Low Conductivity Standards
For low conductivity standards, it is important to limit the amount of carbon dioxide
absoiption into the solution and to reduce the uncertainty associated with this absorption. In order
to achieve this, a mixed aqueous-nonaqueous solvent is used.
When an aqueous solution is used, the major concern is the CO2 content in the atmosphere,
which varies from 300 ppm to 600 ppm or higher, from one time and place to another [22]. This
variation causes a variation in conductivity of about ±0.2 uS/cm, corresponding to an additional
4 % uncertainty for a 5 |iS/cm standard. A mixed aqueous-nonaqueous solvent is desirable,
because the CO2 effect in such a solvent is less than 0.1 |iS/cm [9]. Therefore, the 5 uS/cm and
34
15 uS/cm SRMs consist of KC1 in 30 % n-propanol 70 % water.
NIST has studied solutions of KC1 in 30 % n-propanol 70 % water and solutions of benzoic
acid (BA) in 30 % n-propanol 70 % water [9]. The 100 % pure n-propanol is obtainable on the
open market, and both KG and BA are available as NIST SRMs. The conductivities of the KC1 and
BA solutions are linear functions of their concentrations at low concentration. They may be
expressed empirically as follows [9]:
KKa = 0.35 + 6.38xl04c (20)
and
k-ba= 0.04 + 376c^ (21)
where c is in the units of molality, mol/kg, and K"is in units of uS/cm. The uncertainty of kKC \ is
±0.01 uS/cm and the uncertainty of kba is ±0.2 uS/cm. The temperature effect on the conductivity
was also examined and found to be 2.9 %/°C for KC1 and 2.6 %/°C for BA at 25 °C [9]. Equation
(20) and Eq. (2 1 ) may be used to obtain the concentration for the desired standard. A list of the
required concentrations in molality and in mass fraction for the round values of standard
conductivity is given in the following Table 6.
35
Table 6. Molality and Mass Fraction (Given in Grams Solute per Kilogram Solution, In Vacuum)
of Low Conductivity Standards in 30 % n-PrOH-H 20(
K/0iS/cm) Potassium Chloride (KC1) Benzoic Acid (C6H5COOH)molality/(10"
3mol/kg) n7(g/kg) molality/(10"
3mol/kg) W(g/kg)
5.00 0.072 9 0.005 43 0.174 0.021 3
10.0 0.151 0.011 3 0.702 0.085 7
15.0 0.230 0.017 1 1.58 0.193
20.0 0.308 0.023 0 2.82 0.344
25.0 0.386 0.028 8 4.41 0.538
6. Discussion and Conclusion
The standards described in this report have a variety of characteristics and applications. The
primary standards, described here, are used for high accuracy work and are determined absolutely
by physical and electrical means, without any calibration. The uncertainties associated with the
primary standards are low if the solution is kept free of acid fumes and carbon dioxide.
The industrial standards are given in a form that is easy to use at the expense of high accuracy. The
conductivity of the solvent in equilibrium with atmospheric CCb is included, which causes a
somewhat higher uncertainty. The low conductivity standards are intended for water quality
control. To avoid the problem of the variation of COt content, 30 % n-propanol 70 % water mixed
solvent is used in which the CO2 effect is minimal.
Conductivity measurement is one of the most precise, accurate, and relatively inexpensive
methods for determining the ionic properties of electrolyte solutions. To ascertain the accuracy of a
measurement, a calibrated cell must be used. When calibrating cells, several standards, such as
SRMs, should be measured to validate the calibration. If the cell constants from several
measurements agree to within the measurement uncertainty, then one can be sure that the results are
36
accurate. If the results do not agree, the source of errors must be found and eliminated before
further measurements are made.
37
7. References
1 . F. Kohlrausch and W. A. Nippoldt, Gott. Nach. 415 ( 1 868).
2. F. Kohlrausch and W. A. Nippoldt, W. A., Ann. Physik 138, 280, 370 ( 1 869).
3. F. Kohlrausch, L. Holborn, and H. Dieselhorst, Weid. Ann. 64, 625 ( 1 898).
4. G. Jones and B. C. Bradshaw, J. Am. Chem. Soc. 55, 1 780 ( 1 933).
5. Y. C. Wu, W. F. Koch, W. J. Hamer, and R. L. Kay, J. Solution Chem. 16, 985 (1987); 19, 1053
(1990).
6. Y. C. Wu. K. W. Pratt, and W. F. Koch, J. Solution Chem. 18, 515 (1989).
7. R. A. Robinson and R. H. Stokes, Electrolyte Solutions, 3ld
ed., Butterworths, London (1959).
8. Y. C. Wu, W. F. Koch, D. Feng, L. A. Holland, E. Juhasz, E. Arvay, and A. Tomek, J. Res.
Natl. Inst. Stand. Technol. 99, 241 (1994).
9. Y. C. Wu and P. Berezansky, J. Res. Natl. Inst. Stand. Technol. 100. 521 (1995).
10. Y. C. Wu, W. F. Koch, and K. W. Pratt, J. Res. Natl. Inst. Stand. Technol. 96, 191 (1991).
1 1 . Y. C. Wu and W. F. Koch, J. Solution Chem. 20, 39 1 ( 1 99 1 ).
12. K. W. Pratt, W. F. Koch, Y. C. Wu, and P. A. Berezansky, submitted for publication
13. IUPAC Commission on Physicochemical Measurements and Standards, Pure and Appl. Chem.
53, 1841 (1981).
14. G. Jones and R. C. Josephs, J. Am. Chem. Soc. 50, 1049 (1928).
15. P. H. Dike, Rev. Sci. Instruments. 2, 379 (1931).
16 H. W. Lamson, Rev. Sci. Instruments. 9, 272 (1938).
17. H. C. Parker and E. W. Parker, J. Am. Chem. Soc. 46, 312 (1924).
18. Y. C. Wu, W. F. Koch, and G. Marinenko, J. Res. Natl. Bur. Stand. 89, 395 (1984); Y. C. Wu,
W. F. Koch, and R. A. Durst, NBS Special Publ. 260-53 (1988).
38
19. Guide to the Expression of Uncertainty in Measurement, ISBN 92-67-10188-9, 1
st
Ed.,
International Organization for Standardization, Geneva, Switzerland, 1993.
20. L. Onsager and R. M. Fuoss, J. Phys. Chem. 36, 2689 (1932).
21. Y. C. Wu, W. F. Koch, P. A. Berezansky, and L. A. Holland, J. Solution Chem. 21, 383 (1992).
22. R. Sams, private communication.
About the authors: Rubina H. Jameel and Kenneth W. Pratt are research chemists in the
Analytical Chemistry Division of the NIST Chemical Science and Technology Laboratory.
Yung Chi Wu is a retired senior chemist from the Analytical Chemistry Division of the NIST
Chemical Science and Technology Laboratory.
39
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